Question: Express this quotient in scientific notation: ${\frac{3.780\times 10^{4}} {6.0\times 10^{2}}}$
Answer: Start by collecting like terms together. $= {\frac{3.780} {6.0}} \times{\frac{10^{4}} {10^{2}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.63 \times 10^{4\,-\,2}$ $= 0.63 \times 10^{2}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.63$ is the same as $6.30 \div 10$ , or $6.30 \times 10^{-1}$ $ = {6.30 \times 10^{-1}} \times 10^{2} $ $= 6.30\times 10^{1}$